Transmission systems find a variety of applications. One application is in bicycles, particularly to improve upon derailleur-based bicycle drive trains. A derailleur-based drive train typically includes a bottom bracket, crankset, one to three front chain rings, chain, front derailleur and/or chain guide, cassette, and rear derailleur. As the rider drives the crankset, the front chain ring drives the chain. The chain runs to the cassette and turns the rear wheel of the bike. The chain then runs through the rear derailleur as it returns back to the front chain ring. The rear derailleur moves across the cassette to move the chain from gear to gear, changing the ratio between input and output as the rider shifts gears. Similarly, a front derailleur moves across the chain rings to move the chain to each of the chain rings. These components are typically exposed on the bicycle, subjecting them to damage and contamination, and require a high degree of maintenance. This is particularly a problem with mountain bicycles, which have been developed for riding over rugged terrain.
Other applications for transmission systems include turbines, for example, windmill turbines, exercise equipment, internally geared hubs, automotive and motorcycle transmissions, industrial equipment and tools.